R2-based Hypervolume Contribution Approximation

TL;DR

This paper introduces a novel R2 indicator-based hypervolume contribution approximation method that efficiently estimates contributions by focusing on the relevant region, outperforming traditional and Monte Carlo methods especially in high dimensions.

Contribution

The paper proposes a new hypervolume contribution approximation method based on the R2 indicator that directly targets the contribution region, improving efficiency and accuracy over existing methods.

Findings

The new method outperforms traditional and Monte Carlo methods in accuracy.

It is computationally more efficient in high-dimensional spaces.

The method effectively identifies solutions with smallest hypervolume contributions.

Abstract

In this letter, a new hypervolume contribution approximation method is proposed which is formulated as an R2 indicator. The basic idea of the proposed method is to use different line segments only in the hypervolume contribution region for the hypervolume contribution approximation. Comparing with a traditional method which is based on the R2 indicator to approximate the hypervolume, the new method can directly approximate the hypervolume contribution and will utilize all the direction vectors only in the hypervolume contribution region. The new method, the traditional method and the Monte Carlo sampling method together with two exact methods are compared through comprehensive experiments. Our results show the advantages of the new method over the other methods. Comparing with the other two approximation methods, the new method achieves the best performance for comparing hypervolume contributions of different solutions and identifying the solution with the smallest hypervolume contribution. Comparing with the exact methods, the new method is computationally efficient in high-dimensional spaces where the exact methods are impractical to use.